The guy (Drew Murray) doesn't understand the meaning of AAA or AAAA period from the sounds like it.
AAAA simply means a much higher budget than your typical AAA title. For example a game like GTA V, Call of Duty, God of War, Bloodborne, Gears 5, or Last of Us Part II is a typical AAA game with a budget ranging from 50 million to around 150 million.
An AAAA game could be around and over 300 Million budget. Halo Infinite could be considered as a AAAA game since its costing around 500 milllion on development alone.
It was listed as AAAA game under the jobs at their website simply to indicate that that's what the potential employee would be working on, a game of that high quality caliber and budgets. You can't put random shit on job description, so I am sure the recruiter didn't just came up with it. You can't put random fluff on job descriptions, and I am sure there is someone else that checks that stuff before a job posting is posted.